So the course request for next fall is coming up and I was looking for some advice.

So here are my options.

Take Complex Analysis: Supposedly useful for...Quantum maybe? Higher level stuff like fluid dynamics and chaos? Just looks good to grad schools? The professor is supposedly very good. Downside, workload for the class is unknown. Unknown territory for me.

Take Linear Algebra: Quantum is written in the language linear. Matrices abound. Potentially a 4 credit hour GPA booster. Downsides, its at 8am 4 days a week. Already know a lot of the useful material.

Retake Differential Equations: I got a C last time. Major self-esteem killer. Performed okay on tests, but could not keep up with homework. Downsides: Will it make my transcript look any better, will I learn or relearn that much more? Guaranteed to have the same professor as before who I wouldn't hate to have again, but I have mixed feelings for.

Things to consider:

I work about 30-35 hours a week. I know right? But its unavoidable. I am also gonna be taking Quantum and E&M the same semester. Griffiths for both. It's possible I could do two of the 3 above options, though I am not sure which two (or one) to take. This is gonna be the same time I am applying for grad school and finishing prepping for the GRE.

Well, it depends on what sort of physics you want to get into and what you've previously taken.

If you don't know LA, then you gotta do it first. It's too important, particularly in QM. But if you have seen it before and want to be introduced to something else, Complex Analysis pops up a lot in QFT and is extremely useful. As for DE's, you should re-study that on your own time.

Last edited by fastones3 on Sun Mar 22, 2009 10:55 pm, edited 1 time in total.

One of the most beautiful classes I"ve taken as an undergrad was a complex analysis class. There's a lot of really interesting, deep stuff going on there plus if you're interested in theory, QM, QFT, and a lot of other topics in PDE's -- they're all rooted in Complex Analysis. Take that!

I feel like I've had a decent treatment of a lot of the topics in linear algebra from what I've done vector calculus, classical mechanics, and even some of the eigenvalue business in differential equations. So I'm not sure what all that counts for and what else remains.

As for what physics I'm into, right now I'm mostly a computational condensed matter guy, but who knows what the future holds. I've never felt a big draw towards astro or HEP. I like the scales in between a bit more.

If your previous treatment of LA included things like inner product spaces, hermitian/unitary/orthogonal operators, diagonalization problems (in the context of eigenspaces) then take complex analysis.

If the stuff I just mentioned sounds kind of foreign, I'd take the linear algebra class. All this stuff will arise in quantum (though I don't know how in depth Griffith's quantum book is on the math - my school's undergrad quantum book has a bit more, I think). Certainly I think LA abounds more in physics than complex analysis (at first glimpse) - at least, at the undergraduate level of things. I'd probably save complex analysis for later when you're more familiar with things like quantum - then you'll appreciate it more.

But either way you go, both are good topics and full of interesting things.

If a C is a pass at your school, I wouldn't worry about it, but you really do need differential equations for basically all of physics. Maybe just study that more on your own time because I really don't know any area of physics where they arent really important.

Take linear algebra. The topics mhazelm listed are really basic/general stuff, so if you dont know those already, you really need to. Basic linear algebra concepts like those are essential to really understand quantum well. Griffiths QM isn't that great, Shankar is a little better at the begining, but the math gets really weak later; CT, Sakurai, or LL are decent with the math though, so knowing linear algebra will be really useful to understand them well.

Oh ? I was under the impression it was a standard-type text. I know my University has used it as long as I've been here.

So the consensus is generally that linear is important and what you pick out of vector calc and mechanics is insufficient for use in linear algebra? Guess I'll put it on the agenda then. Though I wonder at how intense a workload QM, E&M, and a linear combination of (c1)Linear Algebra + (c2)Complex Analysis would be if c1, c2 are an element of R >= 0 ?

Oh ? I was under the impression it was a standard-type text. I know my University has used it as long as I've been here.

So the consensus is generally that linear is important and what you pick out of vector calc and mechanics is insufficient for use in linear algebra? Guess I'll put it on the agenda then. Though I wonder at how intense a workload QM, E&M, and a linear combination of (c1)Linear Algebra + (c2)Complex Analysis would be if c1, c2 are an element of R >= 0 ?

nathan12343 wrote:Landau & Lifschitz? My condolensces to the undergrads who have to use that book. That's like learning junior level E&M from Jackson.

Thats a graduate-level textbook I would like to see if anyone can find a syllabus of an undergrad class using that textbook. Sakurai is also a grad book. Why are any of those books being brought up when the OP was asking if he even should take linear algebra?

Thats like a linear algebra student contemplating relativity and suggesting he start with the Thorne,Wheeler book.

nathan12343 wrote:Landau & Lifschitz? My condolensces to the undergrads who have to use that book. That's like learning junior level E&M from Jackson.

Thats a graduate-level textbook I would like to see if anyone can find a syllabus of an undergrad class using that textbook. Sakurai is also a grad book. Why are any of those books being brought up when the OP was asking if he even should take linear algebra?

Thats like a linear algebra student contemplating relativity and suggesting he start with the Thorne,Wheeler book.

We used both of them for parts of several of my undergrad QM courses. I also think most students of relativity do start wtih Wheeler et al's Gravitation, as the begining of it is very introductory and it takes 100s of pages before it actually gets into non introductionary stuff, but maybe thats just from my undergrad background.

thisiswhoiam wrote:We used both of them for parts of several of my undergrad QM courses. I also think most students of relativity do start wtih Wheeler et al's Gravitation, as the begining of it is very introductory and it takes 100s of pages before it actually gets into non introductionary stuff, but maybe thats just from my undergrad background.

What school did you attend? Were these the first two introductory QM courses?Were you taking grad classes as an undergrad?

I'm not able to speak to what's needed for grad success, but I have to recommend Linear Algebra "just because." It really does cover a whole bunch of stuff that you don't get elsewhere, and besides, it's fun.

One of the things you could do if you don't technically need complex analysis is to audit it or take it P/F so you don't have to worry too much about the extra workload. I'd suggest taking Linear for a grade though, since it's really not at all difficult - but unless you're particularly unusually good at self-studying, the ideas/ways of thinking about stuff involved are ones you probably won't pick up elsewhere or on your own, and grad schools know this. The mechanical/computational aspect, for the most part, could be done by a trained iguana (so it shouldn't add a lot to your workload) but you can't really make up for not hearing good explanations of the concepts.

I suppose my tentative plan at this point is to try to find loan money to take Linear as a summer class. What's another $1-2000 dollars among friends eh ?

Even if I was at the level of trained iguana, and I think I'm really only up to well-disciplined skink, its really always the time issue, and I'd prefer to have extra time left over for quantum, E&M, and GRE studying if possible.

Really appreciate the advice guys. I guess I'm gonna take linear now if I can find some loan money.

I think it depends what you're going into. I'm going into atomic physics/quantum optics, and I certainly don't think that complex analysis is necessary (I'm a math and physics major). I've taken complex analysis, and hated it---my friends that like geometry seem to love it, so if you're going into relativity, then take it.

Nevertheless, I'd take linear algebra first and foremost. If you think you can get an A+ in differential equations if you do more work, that would be my second choice. I wouldn't take complex analysis (especially if you haven't taken real analysis yet? real analysis was awesome, though...)---I found it to be a waste of my time.

In fact...I took complex analysis once, dropped it because I was miserable with it, and took it at a different school in the summer. I got an A+...I just found it utterly useless. But some people love it.

On the other hand, we use linear algebra all the time, so I'm with everyone else that learning linear algebra is probably a better call than complex analysis.

I can't really understand hating complex analysis -- it was probably the least offensive math class I've ever taken. You prove some neat things, it has plenty of applications, and it's easier than most math classes (that seems to be true across the board, but it's possible to make it painful).

I talked it over with my adviser/boss and I discovered that my department will be teaching a "Math Methods" course for the first time in some years this summer. Well the times conflicted with linear algebra, and my adviser's advice was to take the math methods course since he said they would be covering the useful material from linear algebra among a great many other things. He has previously taught the class you see.

So I believe I will take the math methods course this summer on his prompting. He may also be the professor so that would also be cool.

I am still slightly debating taking Complex or retaking differential equations. As of now Complex is on my course request for the fall. I have reservations about the DEQ prof, but he's known evil. The Complex prof is supposed to be very good but I've never had him of course and I know some other people who are going to be taking the class who are friends but are curve ruiners.

I talked it over with my adviser/boss and I discovered that my department will be teaching a "Math Methods" course for the first time in some years this summer. Well the times conflicted with linear algebra, and my adviser's advice was to take the math methods course since he said they would be covering the useful material from linear algebra among a great many other things. He has previously taught the class you see.

So I believe I will take the math methods course this summer on his prompting. He may also be the professor so that would also be cool.

I am still slightly debating taking Complex or retaking differential equations. As of now Complex is on my course request for the fall. I have reservations about the DEQ prof, but he's known evil. The Complex prof is supposed to be very good but I've never had him of course and I know some other people who are going to be taking the class who are friends but are curve ruiners.

KS

IMHO, you either take a Math course offered by and meant for Math ppl, which means the stuff is done in some depth and rigor, or you pick the stuff up on the side while doing, say QM. The so called Math Method courses offered by Physics and other departments tend to be the skim-the-surface-and-get-a-"feel"-of-stuff kind which is easily self studied and much more effective when done in an appropriate context.

I took a math methods class last year which was actually very useful. It was as mathematically rigorous as an "applied" math course in the math department, but specifically focused on topics of interest to physicists. It is definitely much better than picking up topics peripherally. That said, for the "core" math courses (calc, linear, DEs) I would still recommend taking the math offerings.